Symmetries of value.
Standard decision theory ranks risky prospects by their expected utility. This ranking does not change if the values of all possible outcomes are uniformly shifted or dilated. Similarly, if the values of the outcomes are negated, the ranking of prospects by their expected utility is reversed. In set...
| Published in: | Nous (0029-4624) Vol. 60; no. 1; pp. 16 - 38 |
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| Format: | Article |
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Wiley-Blackwell
Mar2026
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=191298365&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 191298365 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00294624 D97 jtl: Nous (0029-4624) issn: 00294624 maglogo: Y pubinfo: dt: Mar2026 vid: 60 iid: 1 pid: 480 pub: Wiley-Blackwell artinfo: ui: 191298365 10.1111/nous.12549 ppf: 16 ppct: 22 formats: fmt: – @attributes: type: T – @attributes: type: C – @attributes: type: P size: 536KB tig: atl: Symmetries of value. aug: au: Goodsell, Zachary affil: Philosophy, National University of Singapore, , Singapore su: Expected utility Utility theory Affine transformations Negation (Logic) Decision theory Axioms sug: subj: Expected utility Utility theory Affine transformations Negation (Logic) Decision theory Axioms ab: Standard decision theory ranks risky prospects by their expected utility. This ranking does not change if the values of all possible outcomes are uniformly shifted or dilated. Similarly, if the values of the outcomes are negated, the ranking of prospects by their expected utility is reversed. In settings with unbounded levels of utility, the expected utility of prospects is not always defined, but it is still natural to accept the affine symmetry principles, which say that the true ranking of prospects is unchanged by shifts and dilations, and is reversed by negation—even in hard cases where expected utilities are undefined. This paper investigates the affine symmetry principles and their consequences. The principles are found to be surprisingly powerful. Combined with orthodox axioms, they assign precise utility values to previously problematic cases: for example, ln2$\ln 2$ to the Pasadena prospect (Nover & Hájek, 2004) and −1/2$-1/2$ to the alternating St Petersburg prospect. They also have important structural consequences, notably vindicating Colyvan's (2008) Relative Expectation Theory. The paper then establishes the consistency of the affine symmetry principles. In light of their fruitful consequences, this consistency result supports the adoption of the affine symmetry principles as fundamental axioms of decision theory. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Nous (0029-4624) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Nous (0029-4624) holder: Wiley-Blackwell dt: @attributes: year: 2026 holdings: @attributes: islocal: N |
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